{
 "cells": [
  {
   "cell_type": "code",
   "execution_count": 1,
   "id": "e42fefb2",
   "metadata": {
    "slideshow": {
     "slide_type": "slide"
    }
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "SparsePauliOp(['II', 'IZ', 'ZI', 'ZZ', 'XX'],\n",
      "              coeffs=[-1.05237325+0.j,  0.39793742+0.j, -0.39793742+0.j, -0.0112801 +0.j,\n",
      "  0.1809312 +0.j])\n"
     ]
    }
   ],
   "source": [
    "from hydrogen import pauli_operator\n",
    "\n",
    "H2_op = pauli_operator()\n",
    "print(H2_op)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 2,
   "id": "f143f825",
   "metadata": {
    "slideshow": {
     "slide_type": "fragment"
    }
   },
   "outputs": [],
   "source": [
    "import numpy as np\n",
    "\n",
    "min_eigen_exact = min(np.linalg.eigvalsh(H2_op.to_matrix()))"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 3,
   "id": "7af9a830",
   "metadata": {
    "slideshow": {
     "slide_type": "slide"
    }
   },
   "outputs": [],
   "source": [
    "from qiskit.algorithms.optimizers import SPSA\n",
    "from qiskit.circuit.library import EfficientSU2\n",
    "from qiskit.primitives import Estimator\n",
    "\n",
    "estimator = Estimator()\n",
    "ansatz = EfficientSU2(2)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 4,
   "id": "4aa2a0d4",
   "metadata": {
    "slideshow": {
     "slide_type": "fragment"
    }
   },
   "outputs": [
    {
     "data": {
      "image/png": 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T+Wr9h8deY8ai8dz09LlMnHWdn7KoO0/zn/nJo9w+KYUxL6Zy98s9Wf3L4mOvMferl7j1uSTGvJjmpyzkbHhaA0dt37WRwY825NV/33fsNivXgDf5L1jxKrdP7sCdL3RhzIuplJWXAtb+DBDPayBnz2Yemp7OmBfTuH1SCtMXPkhVlftYJKv1gKc5f7rqDe58oQtXPBzMvOX/V+017LpedAojasDK2wZG5H+UVdeLjttDs2TJEn+H4DOT54zioev/SVJ8Gp+ueoMZix7iil63kRB7Hq89sO7Y4z74cgohQQ14889Z5BVuZdzUPqS1SycqohmjB0+mdfNOrPhpvt/yqCtP8++SeBEj+j9Og5BwsnMzeODvF/Pe47mEh0bw+4vvJym+W7VGFuvwtAYAKirL+b+5o+nbeUi1261cA57mv+LHf/PFD/9i2thviQhvzL7iPQQFuc8KYeXPAPG8Bv7x8Xj6dh7CkH7jKCsv5Z6pvViddDl9OlxluR7wNOf2CT34y4j3eW/Js6e8hl3Xi05hRA1YedvAiPzB2utFx+2hsausnWsJbxBJUnwaAAN63srKzAWUV5Sd8tgvM+Yw+IK7AGgRnUjXdpfy9Y8fmRmu4bzJv3fKQBqEuK++mxjXBVwu9hfvMTNc8QFvagDgnc//l4u7DiM+pg4XLKmHvMn//S8nM3LARCLCGwPQJDKWoEAde2J13tRAAAEcOrwfgCPlh6msLKdZVAszwzWENzm3a5lK6+YdCAg4ddPHjutFpzCqBqy6bWBU/mDt9aLj9tDYVV7hVrbmbai2O/BIWQkFB3ae8tjd+3bQvOnxi5TENW3D7n1nOLdvPedN/idavOafxEW3rbY8xJq8qYGNO74jc/tKnh/9OW9//qSJUfqON/nv2JXJppw1vP35k5RXHmFAj1sY0m+cidGKL3hTA/9z7f/x+BtXs/Dbv1NcUsTN/R8nKb6bidEao66f/Sez43rRKYyqgRNZadvAqPytvl7UQGMjKef24bk7jx/z+YcnYv0Yjfm8zf+HzV/w9udP8vydnxOgX8jbgic1UFpWwrR5d/P4LR/a7v93T3ugsqqC/MKtvHj3VxQfLuLBv19Ci+i2nN9xsFmhio94WgMLVrxKerfhDL/sEYqKdzN+ejrntepFj+QBZoVqGKev+8TYGrDitsHZ5m+H9aIGGptoEd222rdJh0oPUFp2iJio+FMee06Tc9lVtP3Y4QX5Rdvokfw702L1BW/yB8jI/pIp79/G/7ttIa3OOc+sMMWHPK2BvL3Z7N63g/HT0wEoPrwPl6uK4sNFTLjxTVNjNpK3nwHp3YYTFBhE44gYeqdcxcYd32qgsThvamDBir/xzwmbAGgaeQ69U64iI3uZ5QYabz/7a2PH9aJTGFUDYM1tAyPyt8N6Ub+hsYmk+DSCA0P4ftPnACxc8SqXpN5ASHDoKY+9uOswFq2cDrh3Va7PXkbfzteZGa7hvMl//ZaveP69kfzvqH/TrqX9znbnVJ7WQGKLLnz4xB7eeXQb7zy6jaEX3ccVvW63zId2bbzpgfRuN7Hm508B9+8nMrKX0baFesHqvKmBFtFtWfOLuwYOlx1iXfZS2sR1NjVeI3iT8+nYcb3oFEbVgFW3DYzI3w7rRQ00NvLITf9i5iePcOtzSWRkL2P04Mk1Pm7YpeMpqzjMLc+245F/XMHYIa/QOCLG5GiN52n+L3xwB+UVR5g85zbGvJjGmBfT2Jq3weRoxRc8rQG78jT/P1z8AEXFu7hjckfuebknvVIGcknqMJOjFV/wtAYm3Pgmn6yayZgXU7nn5Z50S7qc9LQbTY7WGJ7mvHj1LIY/lcDy9R/w1mdPMPypBLJ2rgXsu150CiNqwMrbBkbkb3U65MxGElt04dU/rTnj48JDI/jLiDkmRGQuT/N/8+HNJkQj/uBpDZzolt894Ztg/MDT/ENDwiz1zZt4ztMaSIrvxstjvzEhIt/zNOcreo3iil6jarzPrutFpzCiBqy8bWBE/iey4npRe2hsLjgolIMle2u8qGBNZiwaz3tLnyUyvKkJ0fmet/nP/eolps67W9/M2YjTa8DpnwHizB7wNufTUU9Yk5E1YMWecFr+AS6Xy+XvIKS6yjJYOtXfUXgnfRwEeXe46mlpGfjGxHmw/zA0Docnh/o7mtOzWg2oB9QDRnN6DTg9f19RD/iWesA/PaA9NCIiIiIiYlkaaERERERExLJ0UoB6KDDEvcvOSgJDjH89py8Dp7NaDagH1ANGc3oNOD1/UQ04PX9vaKCphwIC6v8xuL6mZSBOrwGn5y+qAafnL6oBp+fvDR1yJiIiIiIilqWBRkRERERELEsDjYiIiIiIWJYGGhERERERsSwNNCIiIiIiYlkaaERERERExLI00IiIiIiIiGVpoBEREREREcvSQCMiIiIiIpalgUZERERERCxLA42IiIiIiFiWBhoREREREbEsDTQiIiIiImJZGmhERERERMSyNNCIiIiIiIhlaaARERERERHL0kAjIiIiIiKWFezvAORULhdUlfs7Cu8EhkBAgHGvp2UgVqsB9YB6wGhOrwGn5y+qAafn7w0NNPVQVTksnervKLyTPg6CQo17PS0DsVoNqAfUA0Zzeg04PX9RDTg9f2/okDMREREREbEsDTQiIiIiImJZGmhERERERMSyNNCIiIiIiIhlaaARERERERHL0lnORGysrAJy90FOIeQWQUmZ+/aSMliSCQnR7r+GOiuP2FRlFeTtc/fAzpN64LMN7vpv1Qwahfk1TBGfqaqC3QfdPfBrYfUe+E/Gbz0QDU0a6pTTYl0aaERs6Ne9sHwTrN0O5ZWn3l9eCQvWuv87AOjQEvolQ0pLCNQKTWxg9wH4ZjOs2gKHy069v7wS/rP++L/bxkLfZEhtBcFB5sUp4iv7SmBllvvvwOFT7y+vhM9+PP7vFk2gX3vokQhhIaaFKWIIDTQiNrL7AMz5DrJ3e/4cF5CZ6/6LbQTX94b2cT4LUcSnDhyGuWsgY4d3z9uyx/03PwyG9IBurfVttVhTaTksWgsrsqDK5fnz8vbBB6vdX3YNTIWLkyFQP0wQi9BAYyMZ2ct4aHp6tdvCQiNIiE2mf/eRXNf3XoKC7Pt/uZPzr3LBVz/Dxxk175Hx1J6D8LcvoG97uKYbNLDYt3ROrgFQ/t9vg7mrjx9SUxcHS+Gtb2DdDhjWCxqFGxaeKZxeA+DsZbApH2Z/C0WH6v4aRypg/vewfgcMPx9io4yLzyxOrgFwZv72ykYASE8bTu+Uq3DhouhgPp9//xbTFz7Ajt0buf8PM/wdns85Lf/KKnhnhfvwMqN8sxm274W70iHSgr8tcFoNnMxp+btcsGgdfJFp3Guu/9V96Obdl1tzg85pNVATpy2DFZvhg1Xuve5G2LIHXvgURl8Kbc8x6EVN5rQaOJmT8tfORBtqH9+d/j1GMKDHSK6/dDxT7/2W2MYJfLLqdfYV7/F3eD7npPyrquDtb4wdZo7KKXTvrSk5Yvxr+5qTaqAmTsvf6GHmqKISmPZf2Fts/Gv7mtNqoCZOWgYrs+B9A4eZo0rLYfpS2FZg8AubxEk1UBMn5a+BxgHCQyNIaX0+LpeL3L3Z/g7HdHbO/z/r3YfG+ErePpj1tfsbcCuzcw14ws75f5vtm2HmqAOH4bWl7jMGWpmda8BTdl0Gm3fB+9/57vXLKmDGUthfw4kFrMauNeApO+evQ84cIu+3wo1qGO3nSPzDjvlvK/B+Q+6BKyEq3L2R9uKnnj1nU777UIa+yd7HWJ/YsQa8Ycf8iw7BR2u8e05demD3AfhkPVzb3fsY6xM71oC37LYMjpTD7JXe7ZmpSw+UlLkPZ7vjYuufLMNuNeAtu+bviIGmoKCASZMmMW/ePHJycoiNjWXo0KE888wzjBs3jjfeeINp06YxduxYf4dqiNLyEvYfKsDlch8zuXDldLJ2riWlVW8SYi2+VeoBJ+RfUfnbSszLPSdR4e5rDXhrwVr3qZ2jI71/rj84oQZOxwn5u1zuM/od8XLPSV17YNlG6NoKEmO9f64/OKEGzsQJy2DhOij08gQAde2BH3PcJ97omej9c/3FCTVwOk7K3/YDzbp16xg4cCD5+flERETQsWNHcnNzmTp1KtnZ2RQWFgKQlpbm30AN9NZnE3nrs4nVbuvXeSj3DvmbnyIylxPyX7cDdh0w7/2OVMCyn2FoT/Pe82w4oQZOxwn5b98LP+eZ934u4PMfYXT6GR9aLzihBs7E7stg/2H33nMzLd4APdpYZy+N3WvgTJyUv60HmoKCAq6++mry8/N58MEHmThxIo0aNQJg0qRJPPzwwwQHBxMQEEDXrl39HK1xBvUZzcVdh1FRVc7WvA3MWfY8BftzCA05frqqp9+5kSpXFY+PfP/YbQdKCrlzSidGD57C5d1v9kfohvAk/w1blvPozIGnPLeisoyqqkoWTzqLcx+b4JtN5r/nqi0wKA0aWOBTQz2gHvCFjbnuEwQ0s8CeSqf3ANi/D7718jozRthz0P2bnWSLXKvM6X1g9x44kQU2Tepu3Lhx5OTkMHbsWKZMmVLtvgkTJvDuu++SkZFBYmIiUVEWPC9nLeJj2tM9uT8AvVMG0jmxH/e/2o+X597FYyPeA+Deoa8y+oUuLFk7m8u6DQdg2kf30Cmxn6WbFzzLv0vbi1j4dPVTFxXsz+WeqT259sL6fehhbhFs9cMZZ0rLYe02OD/J/Pf2lnrA3j1QcsQ3Z/Y7Exfub8Sv7mb+e3vL6T0A9u6DKpf7zGb+8M0m6ww0Tu8DO/fAyWx7lrONGzcyZ84cYmJiePbZZ2t8TI8ePQBITU09dtvRAah37940aNCAAKvsVz2NTm0upH/3kSzLmMNP21YA7h+DPThsJq/MH0vB/ly+Wv8h67OXcd/Q6X6O1ng15X+ysoojPPnWUDq36cdNlz9qcoTe2bzLf++d5cf3PhvqAXv1wLYCqKjyz3tn7fbP+54tp/cA2KsP9h6EfSX+ee+s3dY986XT+8BOPXAy2w40s2fPpqqqiptvvpnIyJqPDwgPd18C+sSBJisri7lz5xIXF0evXr1MidUMN/d/nMDAIN5c/Ndjt/VKuZJLul7P87NHMG3e3Tww7HWiIpr5MUrfqSn/E7089y7KyksZf8MscwOrg5xC/733r35877OlHlAPGCG3yH0xWytyeg+AffrAn5/Fh464zzBoVU7vA7v0wMlsO9AsWbIEgPT02n/BmZOTA1QfaC6++GLy8vJYsGAB/fv3922QJoqPSSI99UbWZn3Bhi3Lj90++uop7NybRa+UgfTpMMiPEfpWbfkDfPT1VL7buIgnR80nLLQOp34xWU6R/9579wHvzypVX6gH1ANGKK+EXfv99/5nw+k9APbpA38O9eDfHjxbTu8Du/TAyWz7G5rt290HWLdu3brG+ysqKvjmm2+A6gNNYKDxM17Pnj3Jz8/3+PGhweHMGGv8qUuGX/4YS9fN5s3P/sqUu5YC7osstYhuS2Jcl7N67fbJ7SmrMO6qW75YBjXlvy5rKa9//DDP/PET4qLbnNXrG70MajPose8Jj2pe431Hry9Qm6iw4//7xJDaH1fb9QlcQOfUXhze7/vTS5lVA+oB6/XApXfNJSaxT433GdUDUHsfDLr2evZsqflwDSNZrQfA2Bowc11oVB+Y1QM9h71Am5431HifGT1wz58msHXVux5GW3dO3x5yWg/ExcWxZo2XFxf7jW0HmkOH3PtDDx+ueaHOmTOHgoICGjVqRGKib0+qnp+fz86dOz1+fFhI3abi1HaX8vnk2g9sbd28g8/OVpGXm0tpuXEH9NZlGXibf37hNp5653ruHDyZ1HaX1iXMaoxeBrUKCKr1Lk+vLxAYWLfrEADs3rOXA3s8r+e6MqMGjKQeMK8Hyitrz9GMHijct9+rz/S6sloPgLE1YNa60Mg+MKsHOh8pr/U+M3rgwMFD9bYHwD7rAvWA52w70MTFxVFUVMQPP/zABRdcUO2+vLw8xo8fD0DXrl19/sP/uDjvTgcSGnyar1bqqRYtWxr+7bQvlZaVMHHWdVzQ8Rqu62vMWTyMXga1qqr9mK8DZ3j7qDD3SqyqCg6U1v64071ObEw0jULLzhDk2bNaH6gHzOuB4NPsSDeqB073Wk0bN6IyPv70TzaA1XoAjK0BM/I3ug/M6oEGobVvvpnRA40iw4lXD9RIPVD3/L3dXj6RbQea/v37s3HjRp5//nkGDBhAcrL7iqirV69m5MiRFBS4z3trxgU1vd19VlkGS6f6KBgf2bxpM0Ghxr2er5fB8g1z2ZKXwc6CTSzLmHPK/TMfyuScpud69ZpGL4PavLQYttdy2uaaDg040RND3N/IHSiFJz7y/r2DA+GXH9cQZMKv76zWB+oB83rgnRWwZmvN9/m6BwC++ORDU65FY7UeAGNrwIz8je4Ds3rg0w3w6fqa7zOjB2a+OoXzWkw58wPPknpAPeAp2w40R68z8+uvv9KpUydSUlIoLS0lKyuLgQMH0qZNGxYvXlzt9zNO9cL/LPN3CKYb0GMkA3qM9HcYddIquvaBxtdaNsWUYcZs6gFraRVd+0Djaw1DITrCP+/tS07sAbBuH7SK9u/7J/j5/X3FiX1g1R44mQ03TdwSEhJYvnw5gwYNIiwsjG3bthEdHc1rr73Gxx9/zKZN7stMa6ARq/HniszfK1ER8H8P2ODyZGJx/uyB6AiIaOC/9xepiW330AB06NCBRYsWnXJ7cXEx27ZtIzAwkM6dO/shMpG6S2kJgQHuK0WbrZPvD5kWOaNzm0FkGBSf4fh/X+ioHpB6ICrcPdT443o0Wg9IfWTrgaY2P/30Ey6Xi+TkZBo2PPUMEh9++CEAmZmZ1f7dpk0bevbsaV6gIjVoHA5dW8G6Hea+b7NI9zAl4m/BQXB+O/jvT+a+b2gQ9G5r7nuK1KZvMrz3rX/eV6S+ceRAs2HDBqD2w82GDRtW479vvfVWZs2a5dPYRDzRN9n8gebCJPeeIZH64MIk+CITXCbuqezeBsL98GNXkZp0bw3//gEO+/6kk8ckNYe4xua9n4inbPsbmtM500Djcrlq/NMwI/VF0jnm7vaPiYR+55n3fiJnEh0JF5tYk2EhcGVX895P5ExCg2GQiT8DDgyAa7qZ934i3tAeGhvJzs3gpQ/vpOTIQZo3ac3Dw99m+66fePT1gSTEnsdzoz+jaeQ5fLrqDeYuf4kduzcyZvAUhl5037HXmLFoPMsy5tA+vjtPjprvt1zqwtP83/jkMVZmLiDwtwtU3njZn0lPuxGwTv4BAXB9H3hukTnfzg0/HxpY4NPC0xqY9N4oftj8OY0jYgHokTyA0YMnA9apgZp4mv8Ts4aQV3j8NGFb89fzxK3zubDTNcz96iUWrPgbYaGRvPbAOv8l44FBqZC5E/Yc9P17DelR94sQmsnTGsjZs5lpH93NvuLdVFZVMKL/X7k0zX3leSvVABiz7rPqevHC9pCxAzbv8v17Xd7R/fu1+siIGrDytoER+Vt9vWiBTRTjLVmyxN8h+MTkOaN46Pp/khSfxqer3mDGooe4otdtJMSeV22l1D6hB38Z8T7vLXn2lNcYPXgyrZt3YsVP880L3CCe5n/9peO5feDTABTs38kdkzvQvX1/GkfEWCr/xuEwrBe89Y3nzzl6kbQzXXjtROkdoF1z72LzF09rANx1cOKH+VFWqoGTeZr/E6OOX3zil1/X8OjrV9LrvCsB+P3F95MU341X/32fydF7LzQYbroAXvkvVFZ59py69EDXVtb57YynNTB5ziiu6HUbV/X5I/uK93DPyz3pnNiPmMbxlqoBMGbdZ9X1YmAA3Hi++9ozh4549py69EBCNFzRxfv4zGJEDVh528CI/MHa60VHHnJmR1k71xLeIJKk+DQABvS8lZWZCyivOPXr+3YtU2ndvAMBAfb5v9+b/CPDmxz778NHinHhosrl4dZQPdO9jfubY0+9+Kn7QmpnuvDaUT0T4WqLHGLgTQ3YUV3z/3TVTC7vPoKQYGv+OCQxFkb18/z3Xd72QFJzGHGhNU7V7E0NbMnLoHfKVQA0iYylbctUlq079aJ69Z1R6z4rrxebRcKYdPdhkZ7wtgfOiXK/fnBQ3WP0JaNqwKrbBk7f/jvKkXto7CivcCtb8zYw5sW0Y7cdKSuh4MBO/wVlIm/z/+jrqSxY8TcK9uVw/7DXaRp5jkmRGu+SFPeKZu5qY0/l3Lc9/L6ndU4E4HUNLH+ZT1e9wTlNz2XUFU8dWxlYVV0+A46UH2bputm8dPdyEyL0nS6t4I+XwKzlUFZp3Ot2iodb+7n3BFmBNzXQPqEHX/zwDjekTyBv7xYyt60grmkb84I1iNPXfUed2wzu6Q+vLTX2dOatot3DTGSYca9pNCNrwIrbBobmb+H1okU+psUTKef24bk7Fx/79x+eiPVjNObzJv8h/cYxpN84snMzeG72CHom/46oiHp6cLAH+rZ3r3hmr4S8/Wf3WpENYFhvSD3XmNjM5GkN3D7waaIbtSAwMJCvN3zEYzMHMuvhzYQ3iDQrVJ/w9jPgq/UfkhCbTGKLenwsiYc6xsOEQTD7W8jefXavFRoMV6e5zyZolYH+KE9rYMINb/LawgcZ82IazZu2plv7ywkKtOYmgdPXfUe1ioY/D4IPV5/9WTADA6B/J/hd5/q7Z+ZERtWAVbcNjMjf6utF++1zcqgW0W3Zve/4J9ih0gOUlh0iJsoZV8Cqa/7tWqYSExVPRvYyH0foe+c2gwcHwsCu7qHEWyFBcEES/HmwNYcZb2ogpnE8gYHuj79+XYbQMCyKX/f8YlqsvlCXHvh01Uyu7HWHGeGZIqaR+1vqP/SCphHePz8wwF37E66Ci86z3jDjTQ3ERbdh4q1zee2Bdfzvbf/m0OH9tI7rZGa4hnD6uu9kkWEw6iK47SJoUcfTKyfHwf1XwlWp1hhmfFEDVto2MCp/q68XNdDYRFJ8GsGBIXy/6XMAFq54lUtSb7DscfHe8ib/7bsyj/13bkE2WblrObd5R9Ni9aXgIPcPN58YAiMvhPbNT392sqBA97d613WHJ4fADX3q96EFp+NNDezZl3PsvzO3f8uBQ3uJb5ZkWqy+4O1nwM6CLDblrCG923Azw/S5wADolwyPXwN3XgKdE6DhaT4GAwLc19W4ogv89Tr3hmBMI9PCNZQ3NVB0cBdVVe7fB6z+ZTHbd2dyWbebTI3XCE5f99Um9Vz3Hst7B0CPNhAVfvrHxzRynwb9kavh7svd6wWrMKoGrLptYFT+Vl8vWnP/stTokZv+xeT3b2PqvP+hZbMk/nzTO2zL//GUxy1ePYtZi/9CcUkRK36azwdfTuH/3baQpHiL/Pq7Fp7m/4+PJ5BfuJWgwBCCgoIZe90rtG7ewQ8R+05wEPRIdP9VuWDPAcjdB0fKwYV7b0zzKGjRxBrfwHnK0xqYPGcURcW7CAwIokFIOI+P/ICIcOtfLc7T/AE+Xf0GF3X5PRFhUSZHaY7AQOiU4P5zuaDwEOwsgpIyqKpy131sI2jZ1BqnJPeUpzWwMnMhc5Y+R2BgEM2iWvL0Hf+hQcgZtnrrKSPWfXZcLwYEQLtz3H8A+0sgpxCKj7jPChgcBE0bQnz06Yd+KzCiBqy8bWBE/lZfL9roY1wSW3Th1T+tOePjrug1iit6jfJ9QCbzNP+nbl9kQjT1R2AANG/s/rM7T2tg0pj/mhCN+TzNH+COgc/4OJr6IyDAfSaoZtY4FPyseFoDV/X5I1f1+aMJEfmeEes+u64XT9S4ofvPjoyoAStvGxiRv9XXizrkzOaCg0I5WLKXMS+mUVR85l/Kzlg0nveWPktkeFMTovM9p+cvqgFv85/71UtMnXc3jSNiTIhOzODEGvA259Ox22eCUzi9BpyWf4DL5TLwRK9ihMoyWDrV31F4J30cBBm4y1rLQKxWA+oB9YDRnF4DTs9fVANOz98b2kMjIiIiIiKWpYFGREREREQsS4ec1UMuF1SV+zsK7wSGuH94axQtA7FaDagH1ANGc3oNOD1/UQ04PX9vaKARERERERHL0iFnIiIiIiJiWRpoRERERETEsjTQiIiIiIiIZWmgERERERERy9JAIyIiIiIilqWBRkRERERELEsDjYiIiIiIWJYGGhERERERsSwNNCIiIiIiYlkaaERERERExLI00IiIiIiIiGVpoBEREREREcvSQCMiIiIiIpalgUZERERERCxLA42IiIiIiFiWBhoREREREbEsDTQiIiIiImJZGmhERERERMSyNNCIiIiIiIhlaaARERERERHL0kAjIiIiIiKWpYFGREREREQsSwONiIiIiIhYlgYaERERERGxLA00IiIiIiJiWf8fwi7r2qWFFPgAAAAASUVORK5CYII=",
      "text/plain": [
       "<Figure size 1039.79x200.667 with 1 Axes>"
      ]
     },
     "execution_count": 4,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "ansatz.decompose().draw('mpl')"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 5,
   "id": "0a9a4370",
   "metadata": {
    "slideshow": {
     "slide_type": "slide"
    }
   },
   "outputs": [],
   "source": [
    "callback = lambda nfev, params, fval, step, acc: print(f'Evaluation {nfev}: {fval}')\n",
    "optimizer = SPSA(callback=callback, maxiter=1000)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 6,
   "id": "f670f56d",
   "metadata": {
    "slideshow": {
     "slide_type": "fragment"
    }
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Evaluation 3: -1.2002016972348648\n",
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      "Evaluation 768: -1.857030999608126\n"
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     "output_type": "stream",
     "text": [
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      "Evaluation 2400: -1.857167432716237\n",
      "Evaluation 2403: -1.85716851624385\n",
      "Evaluation 2406: -1.8571391676543427\n",
      "Evaluation 2409: -1.85713688007459\n",
      "Evaluation 2412: -1.8571576656174171\n",
      "Evaluation 2415: -1.8571952224797539\n",
      "Evaluation 2418: -1.8571952483300374\n",
      "Evaluation 2421: -1.8572003694614267\n",
      "Evaluation 2424: -1.857220832783021\n",
      "Evaluation 2427: -1.8572401746665417\n",
      "Evaluation 2430: -1.857219922546135\n",
      "Evaluation 2433: -1.857216552357656\n",
      "Evaluation 2436: -1.857212674375005\n",
      "Evaluation 2439: -1.8572173477912872\n",
      "Evaluation 2442: -1.8572281655108371\n",
      "Evaluation 2445: -1.8572146475827533\n",
      "Evaluation 2448: -1.8572211558944485\n",
      "Evaluation 2451: -1.8572223545038382\n",
      "Evaluation 2454: -1.8572299376067487\n",
      "Evaluation 2457: -1.857226606486011\n",
      "Evaluation 2460: -1.85721997505871\n",
      "Evaluation 2463: -1.857213282408927\n",
      "Evaluation 2466: -1.857207495922548\n",
      "Evaluation 2469: -1.8572056146271259\n",
      "Evaluation 2472: -1.857211208595903\n",
      "Evaluation 2475: -1.8572085652614432\n",
      "Evaluation 2478: -1.857208450374663\n",
      "Evaluation 2481: -1.8572085299338543\n",
      "Evaluation 2484: -1.8572081716891222\n",
      "Evaluation 2487: -1.8572107343364577\n",
      "Evaluation 2490: -1.8572155426354298\n",
      "Evaluation 2493: -1.857214120463022\n",
      "Evaluation 2496: -1.857211695349422\n",
      "Evaluation 2499: -1.8571984416444058\n",
      "Evaluation 2502: -1.8572041759379312\n",
      "Evaluation 2505: -1.857203930958376\n",
      "Evaluation 2508: -1.857198677531339\n",
      "Evaluation 2511: -1.857197169341878\n",
      "Evaluation 2514: -1.8572127239144747\n",
      "Evaluation 2517: -1.857217320526624\n",
      "Evaluation 2520: -1.8572170134550476\n",
      "Evaluation 2523: -1.8572158832930739\n",
      "Evaluation 2526: -1.8572085045830542\n",
      "Evaluation 2529: -1.8572110879413908\n",
      "Evaluation 2532: -1.8572167006841405\n",
      "Evaluation 2535: -1.8572031393337958\n",
      "Evaluation 2538: -1.8572011633803784\n",
      "Evaluation 2541: -1.8571934362683729\n",
      "Evaluation 2544: -1.8571822321905023\n",
      "Evaluation 2547: -1.857184525770129\n",
      "Evaluation 2550: -1.8571836070965986\n",
      "Evaluation 2553: -1.8571932973803817\n",
      "Evaluation 2556: -1.8571834481431448\n",
      "Evaluation 2559: -1.8571863853049582\n",
      "Evaluation 2562: -1.8571935755186726\n",
      "Evaluation 2565: -1.8572015622051359\n",
      "Evaluation 2568: -1.8572013907471918\n",
      "Evaluation 2571: -1.857205134287294\n",
      "Evaluation 2574: -1.857205035702182\n",
      "Evaluation 2577: -1.8571866341976453\n",
      "Evaluation 2580: -1.8571878595252302\n",
      "Evaluation 2583: -1.857183781533952\n",
      "Evaluation 2586: -1.8571837705997338\n",
      "Evaluation 2589: -1.8571825857808668\n",
      "Evaluation 2592: -1.8571693581474225\n",
      "Evaluation 2595: -1.8571687438661875\n",
      "Evaluation 2598: -1.8571686649964159\n",
      "Evaluation 2601: -1.8571684331596878\n",
      "Evaluation 2604: -1.8571728349707801\n",
      "Evaluation 2607: -1.8571740884134775\n",
      "Evaluation 2610: -1.8571730689223898\n",
      "Evaluation 2613: -1.8571544995333624\n",
      "Evaluation 2616: -1.8571620765646\n",
      "Evaluation 2619: -1.8571594448147053\n",
      "Evaluation 2622: -1.8571597988630426\n",
      "Evaluation 2625: -1.8571458636864635\n",
      "Evaluation 2628: -1.857167938690407\n",
      "Evaluation 2631: -1.85717042405572\n",
      "Evaluation 2634: -1.8571766772593161\n",
      "Evaluation 2637: -1.8571777330860972\n",
      "Evaluation 2640: -1.8571621464882464\n",
      "Evaluation 2643: -1.8571762864201888\n",
      "Evaluation 2646: -1.8571785113886594\n",
      "Evaluation 2649: -1.8571814407263803\n",
      "Evaluation 2652: -1.857204832857805\n",
      "Evaluation 2655: -1.8572065897913892\n",
      "Evaluation 2658: -1.857206600772257\n",
      "Evaluation 2661: -1.857204575834536\n",
      "Evaluation 2664: -1.8572039889446312\n",
      "Evaluation 2667: -1.8572089726227583\n",
      "Evaluation 2670: -1.8572007008305305\n",
      "Evaluation 2673: -1.8571968375231156\n",
      "Evaluation 2676: -1.8571967527368938\n",
      "Evaluation 2679: -1.8571992004666056\n",
      "Evaluation 2682: -1.8572013938414826\n",
      "Evaluation 2685: -1.8571906914707792\n",
      "Evaluation 2688: -1.8571727801045506\n",
      "Evaluation 2691: -1.8571788252903014\n",
      "Evaluation 2694: -1.8571776335288641\n",
      "Evaluation 2697: -1.8571775697520272\n",
      "Evaluation 2700: -1.8571812758769581\n",
      "Evaluation 2703: -1.8571813801886443\n",
      "Evaluation 2706: -1.8571868481917728\n",
      "Evaluation 2709: -1.8572141871371977\n",
      "Evaluation 2712: -1.857155346920672\n",
      "Evaluation 2715: -1.8571875034155994\n",
      "Evaluation 2718: -1.8571755646398813\n",
      "Evaluation 2721: -1.8571758730274834\n",
      "Evaluation 2724: -1.8571824914494317\n",
      "Evaluation 2727: -1.857193873023516\n",
      "Evaluation 2730: -1.857202075635989\n",
      "Evaluation 2733: -1.857210165154808\n",
      "Evaluation 2736: -1.8572076018430184\n",
      "Evaluation 2739: -1.8572049971026598\n",
      "Evaluation 2742: -1.857203531824328\n",
      "Evaluation 2745: -1.8572025997918757\n",
      "Evaluation 2748: -1.8572041719347805\n",
      "Evaluation 2751: -1.8572084069889956\n",
      "Evaluation 2754: -1.8572023888915554\n",
      "Evaluation 2757: -1.8572027450575328\n",
      "Evaluation 2760: -1.8572071597183628\n",
      "Evaluation 2763: -1.8572039735773098\n",
      "Evaluation 2766: -1.8572055793983873\n",
      "Evaluation 2769: -1.8571905077184248\n",
      "Evaluation 2772: -1.857190496577559\n",
      "Evaluation 2775: -1.8572017122203912\n",
      "Evaluation 2778: -1.8572084366312545\n",
      "Evaluation 2781: -1.8572066897519004\n",
      "Evaluation 2784: -1.8571971224652428\n",
      "Evaluation 2787: -1.8572240464225607\n",
      "Evaluation 2790: -1.8572235365363436\n",
      "Evaluation 2793: -1.857228139400283\n",
      "Evaluation 2796: -1.8572357908622272\n",
      "Evaluation 2799: -1.857247156659343\n",
      "Evaluation 2802: -1.857256897882841\n",
      "Evaluation 2805: -1.8572624589588012\n",
      "Evaluation 2808: -1.8572459126950902\n",
      "Evaluation 2811: -1.8572460162365712\n",
      "Evaluation 2814: -1.857248338233322\n",
      "Evaluation 2817: -1.8572512065837\n",
      "Evaluation 2820: -1.8572505124751133\n",
      "Evaluation 2823: -1.857250046522623\n",
      "Evaluation 2826: -1.8572405699003218\n",
      "Evaluation 2829: -1.8572416441862287\n",
      "Evaluation 2832: -1.8572237549515336\n",
      "Evaluation 2835: -1.8572229553609598\n",
      "Evaluation 2838: -1.8572223674673545\n",
      "Evaluation 2841: -1.8572339435949439\n",
      "Evaluation 2844: -1.857234328742095\n",
      "Evaluation 2847: -1.8572332668124927\n",
      "Evaluation 2850: -1.8572345788484141\n",
      "Evaluation 2853: -1.8572370243429266\n",
      "Evaluation 2856: -1.8572379205742753\n",
      "Evaluation 2859: -1.8572341743076326\n",
      "Evaluation 2862: -1.8572440963717542\n",
      "Evaluation 2865: -1.8572454268952596\n",
      "Evaluation 2868: -1.8572442306162857\n",
      "Evaluation 2871: -1.8572442120979789\n",
      "Evaluation 2874: -1.8572447005108748\n",
      "Evaluation 2877: -1.857226020680365\n",
      "Evaluation 2880: -1.857220978645945\n",
      "Evaluation 2883: -1.8572215244980326\n",
      "Evaluation 2886: -1.857221971944905\n",
      "Evaluation 2889: -1.857215181567467\n",
      "Evaluation 2892: -1.857205835075024\n",
      "Evaluation 2895: -1.8572139248635549\n",
      "Evaluation 2898: -1.857203195223184\n",
      "Evaluation 2901: -1.8572066637151858\n",
      "Evaluation 2904: -1.8571958427363253\n",
      "Evaluation 2907: -1.8571918110279648\n",
      "Evaluation 2910: -1.857185649795756\n",
      "Evaluation 2913: -1.8571991318746202\n",
      "Evaluation 2916: -1.8571795264575421\n",
      "Evaluation 2919: -1.8571810580338652\n",
      "Evaluation 2922: -1.857196182078168\n",
      "Evaluation 2925: -1.857194749852731\n",
      "Evaluation 2928: -1.857213033963266\n",
      "Evaluation 2931: -1.8572104781642036\n",
      "Evaluation 2934: -1.8572116882051581\n",
      "Evaluation 2937: -1.8572114054133342\n",
      "Evaluation 2940: -1.8572167631172136\n",
      "Evaluation 2943: -1.8572182396524577\n",
      "Evaluation 2946: -1.8572198011118362\n",
      "Evaluation 2949: -1.8572215704116648\n",
      "Evaluation 2952: -1.8572266593485143\n",
      "Evaluation 2955: -1.857230921480217\n",
      "Evaluation 2958: -1.8572347971961463\n",
      "Evaluation 2961: -1.8572284600564348\n",
      "Evaluation 2964: -1.8572285339182606\n",
      "Evaluation 2967: -1.8572295182664162\n",
      "Evaluation 2970: -1.857234101481093\n",
      "Evaluation 2973: -1.8572337402895944\n",
      "Evaluation 2976: -1.8571878257854124\n",
      "Evaluation 2979: -1.857187749123907\n",
      "Evaluation 2982: -1.857189813115094\n",
      "Evaluation 2985: -1.857190276979321\n",
      "Evaluation 2988: -1.8571904431751607\n",
      "Evaluation 2991: -1.857188745211383\n",
      "Evaluation 2994: -1.8572011093547753\n",
      "Evaluation 2997: -1.857201267830064\n",
      "Evaluation 3000: -1.8572091007105938\n"
     ]
    }
   ],
   "source": [
    "cost_func = lambda params: estimator.run(ansatz, H2_op, parameter_values=params).result().values[0]\n",
    "result = optimizer.minimize(cost_func, x0=np.zeros(ansatz.num_parameters))"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 7,
   "id": "a6cf2657",
   "metadata": {
    "slideshow": {
     "slide_type": "slide"
    }
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "{   'fun': -1.8572091007105938,\n",
      "    'jac': None,\n",
      "    'nfev': 3000,\n",
      "    'nit': 1000,\n",
      "    'njev': None,\n",
      "    'x': array([-0.16804134,  0.58689521,  0.3088592 , -2.37589952, -0.33554299,\n",
      "       -1.95694389,  2.64129183,  0.04939797, -2.85366218,  2.56464313,\n",
      "        4.03088657,  1.27105932, -0.03024692,  3.59928397,  0.21859992,\n",
      "       -0.145587  ])}\n"
     ]
    }
   ],
   "source": [
    "print(result)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 8,
   "id": "d67de6fb",
   "metadata": {
    "slideshow": {
     "slide_type": "fragment"
    }
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "-1.8572750302023795\n"
     ]
    }
   ],
   "source": [
    "print(min_eigen_exact)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 9,
   "id": "9d235e36",
   "metadata": {
    "slideshow": {
     "slide_type": "slide"
    }
   },
   "outputs": [],
   "source": [
    "from qiskit_ibm_runtime import Options\n",
    "\n",
    "options = Options()\n",
    "options.execution.init_qubits = True\n",
    "options.execution.shots = 5000"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 10,
   "id": "2603383a",
   "metadata": {
    "slideshow": {
     "slide_type": "fragment"
    }
   },
   "outputs": [],
   "source": [
    "options.environment.callback = []\n",
    "options.environment.job_tabs = []\n",
    "options.environment.log_level = 'DEBUG'"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 11,
   "id": "912dcb0f",
   "metadata": {
    "slideshow": {
     "slide_type": "slide"
    }
   },
   "outputs": [],
   "source": [
    "from qiskit_ibm_runtime import QiskitRuntimeService\n",
    "\n",
    "service = QiskitRuntimeService()\n",
    "backend = service.get_backend('ibm_lagos')"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 1,
   "id": "21daf829",
   "metadata": {
    "slideshow": {
     "slide_type": "fragment"
    }
   },
   "outputs": [],
   "source": [
    "from qiskit_ibm_runtime import Estimator, Session\n",
    "\n",
    "with Session(service=service, backend=backend) as session:\n",
    "    estimator = Estimator(options=options)\n",
    "    cost_func = lambda params: estimator.run(ansatz, H2_op, parameter_values=params).result().values[0]\n",
    "    result = optimizer.minimize(cost_func, x0=np.zeros(ansatz.num_parameters))"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "4b19d9a0",
   "metadata": {},
   "source": [
    "The energes per evaulation are stored in `energies-vqe.json` and retrieved below."
   ]
  },
  {
   "cell_type": "markdown",
   "id": "3ae0ae23",
   "metadata": {
    "slideshow": {
     "slide_type": "fragment"
    }
   },
   "source": [
    "```\n",
    "Evaluation 3: -1.0658799956246998\n",
    "Evaluation 6: -1.1096675267382927\n",
    "Evaluation 9: -1.0142706237256192\n",
    "Evaluation 12: -1.0517553203534658\n",
    "Evaluation 15: -1.0910806641130564\n",
    "Evaluation 18: -1.099400857338864\n",
    "Evaluation 21: -1.046839083072532\n",
    "Evaluation 24: -1.0266394982381541\n",
    "Evaluation 27: -1.0807949769989533\n",
    "Evaluation 30: -1.1132748163678658\n",
    "Evaluation 33: -0.98100438223322\n",
    "Evaluation 36: -1.0482607630007952\n",
    "Evaluation 39: -0.9743416475998952\n",
    "Evaluation 42: -0.9078181580675616\n",
    "Evaluation 45: -1.1157035270120559\n",
    "Evaluation 48: -1.0045905105874828\n",
    "Evaluation 51: -1.0450832043715694\n",
    "Evaluation 54: -1.0476693709899938\n",
    "Evaluation 57: -1.057792338409782\n",
    "Evaluation 60: -1.0250368825796192\n",
    "Evaluation 63: -1.1274344381244423\n",
    "Evaluation 66: -1.0143092551160626\n",
    "Evaluation 69: -1.02223955548793\n",
    "Evaluation 72: -1.018810314294241\n",
    "Evaluation 75: -1.046251121776767\n",
    "...\n",
    "Evaluation 999: -1.779113504536307\n",
    "Evaluation 1002: -1.8010218517658347\n",
    "Evaluation 1005: -1.8221585466818406\n",
    "Evaluation 1008: -1.7773243435410948\n",
    "```"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "id": "3b8069ad",
   "metadata": {
    "slideshow": {
     "slide_type": "slide"
    }
   },
   "outputs": [],
   "source": [
    "print(result)"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "0da92303",
   "metadata": {
    "slideshow": {
     "slide_type": "fragment"
    }
   },
   "source": [
    "```\n",
    "{   'fun': -1.7773243435410948,\n",
    "    'jac': None,\n",
    "    'nfev': 1008,\n",
    "    'nit': 336,\n",
    "    'njev': None,\n",
    "    'x': array([ 2.9743616 ,  1.32176003,  -2.50764169,  1.46563114,  -0.24502706,\n",
    "       4.75714675, 1.76251035,  0.29429557, -2.63338722,  1.22095218,\n",
    "       -0.09407169,  1.16759208,  -2.52594908,  2.01989448,  3.78551471,\n",
    "       2.00617719])}\n",
    "```"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 19,
   "id": "df5a7fbb",
   "metadata": {
    "slideshow": {
     "slide_type": "slide"
    }
   },
   "outputs": [],
   "source": [
    "jobs = service.jobs(session_id=session.session_id, limit=None)\n",
    "energies = [job.result().values[0] for job in jobs if job.done()][::-1]"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 22,
   "id": "6d2e14cf",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "<matplotlib.legend.Legend at 0x1769a1b40>"
      ]
     },
     "execution_count": 22,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
      "image/png": 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",
      "text/plain": [
       "<Figure size 640x480 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "import matplotlib.pyplot as plt\n",
    "plt.style.use('dark_background')\n",
    "\n",
    "plt.plot(range(len(energies)), energies, label='backend')\n",
    "plt.plot(range(len(energies)), [min_eigen_exact]*len(energies), ls='--', label='exact')\n",
    "plt.xlabel('Iteration', fontsize=16)\n",
    "plt.ylabel('Energy', fontsize=16)\n",
    "plt.legend(loc=1)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 20,
   "id": "30cba969",
   "metadata": {
    "slideshow": {
     "slide_type": "fragment"
    }
   },
   "outputs": [],
   "source": [
    "import json\n",
    "\n",
    "with open('energies-vqe.json', 'r') as handle:\n",
    "    energies = json.load(handle)"
   ]
  }
 ],
 "metadata": {
  "celltoolbar": "Slideshow",
  "kernelspec": {
   "display_name": "qiskit-runtime",
   "language": "python",
   "name": "python3"
  },
  "language_info": {
   "codemirror_mode": {
    "name": "ipython",
    "version": 3
   },
   "file_extension": ".py",
   "mimetype": "text/x-python",
   "name": "python",
   "nbconvert_exporter": "python",
   "pygments_lexer": "ipython3",
   "version": "3.10.9"
  },
  "rise": {
   "theme": "monokai",
   "transition": "none"
  }
 },
 "nbformat": 4,
 "nbformat_minor": 5
}
